APPLICATION OF THE PUFEM FOR THE 2D ANALYSIS OF INTERIOR SOUND FIELD WITH ABSORBING MATE- RIALS Jean-Daniel Chazot, Benoit Nennig, Emmanuel Perrey-Debain Universit´ e de Technologie de Compi` egne, Laboratoire Roberval UMR 6253, BP 20529, 60205 Compi` egne cedex, France LAUM UMR6613 CNRS.Universit´ e du Maine, Ave. Olivier Messiaen, F-72085 Le Mans cedex 9, France The paper deals with the numerical simulation of the acoustic field in two dimensional cav- ities in which absorbing materials are present. Though Finite Element Method (FEM) could be employed for this purpose, the discretization level required for achieving reasonable accu- racy renders the method impractical in the mid-frequency range. To alleviate this limitation, the Partition of Unity Finite Element Method (PUFEM) using plane wave functions has been shown to be very effective for solving short waves Helmholtz problems. In the present work, the method is extended for the computation of the pressure wave field within the absorbing media which is modeled as a bulk-reacting material characterized by a complex mean den- sity and a complex speed of sound. Lagrange multipliers are used to enforce the transmission conditions at the air-material interface. Performances of the PUFEM are compared with stan- dard FEM in several examples of practical interests. It is shown that the technique is a good candidate for solving noise control problems of large dimensions. 1. Introduction In this work, we are concerned with the numerical simulation of sound pressure field in en- closed cavities in which absorbing materials are present. The type of applications we have in mind ranges from room acoustics predictions, sound proofing of aircrafts or cars’ passenger compartments to muffler designs in HVAC systems. If standard FEM and BEM can, in principle, be used for this purpose [1], these methods are known to be extremely demanding computationally when the fre- quency increases and are thus limited to ‘low’ frequency applications [2]. To alleviate this difficulty, the last decade have seen the emergence of new approaches in which the solution to the problem is expanded in the basis of oscillatory wave functions. Though this not the place for a complete survey, we can cite the Partition of Unity Method (PUFEM) [3], the Ultra-Weak formulation [4], the Discon- tinuous Galerkin Method [5], the Wave Boundary Element Method [6], the Wave Based Method [7] and the Variational Theory of Complex Rays [8]. Among all these techniques, the PUFEM offers the advantage to be very similar to the conventional FEM and its numerical implementation can be easily adapted to any FEM mesh. Application of the PUFEM using plane waves and/or Bessel functions for the computation of acoustic and elastic waves can be found in recent papers [9, 10]. One direction of particular interest to us is to extend the PUFEM for the analysis of sound field in cavities filled ICSV18, 10–14 July 2011, Rio de Janeiro, Brazil 1